At breakfast, when it's Jo-Jo's turn with his dad, 12 seconds start on the clock, but when the mayor starts showing Jo-Jo all the perks about being mayor, the clock goes back to 12 seconds left when it should be at 5 seconds left.
It is shown that only when the clover and "speck" is moved or stopped suddenly or fast, does it effect the Whos world. When in reality, every time Horton moved the clover, sat it down, talked to it, or walked, the speck would feel vibrations, wind, and ground tremors, at the very least. But maybe this can be explained by the fact it's a fictional world and things don't move like they would in real life.
The mayor explains to his son that the family has been in Whoville for centuries. A few scenes later we learn that the city is planning their centennial. Actually they are celebrating their one hundred years of happiness and peace, so his family could have been there for centuries.
When we first see Jo-Jo, the narrator introduced him as "the smallest Who of all." But seconds later one of his little sisters appears in the same shot and she is clearly smaller than he is. This is because the sister is a baby and therefore supposed to be smaller then Jo-Jo. The term "smallest Who of all" could be a reference to him being small then other Whos his own age (as shown in a deleted scene).
Just before the Mayor is seen for the first time in the movie, the Narrator says his surname is McDodd, even though his wife's surname is O'Malley. However, plenty of human wedded couples don't share a surname and there's no reason to suspect that a wife taking her husband's surname in Whoville is obligatory or even customary.
In order to save the speck of dust, Horton quickly sucks up some water from the pond and swallows it. However, elephants can't drink through their noses. They use them to squirt water into their mouths when they're thirsty. Elephants also can't climb trees, stand upright, hold objects with their front feet, move their ears like hands, or talk. However, Horton is a Dr. Seuss-style elephant from a fictional world, so all these stunts are feasible.
When the mayor is telling Horton about his family, he says "I have a beautiful wife, ninety-six daughters and one son." He doesn't mention his son's name. Yet later in the movie, Horton says "The mayor has one son named Jo-Jo." Unless he and the mayor have another conversation in the movie that we don't see, Horton couldn't have known Jo-Jo's name.
Whoville would have been safe indefinitely had Horton not 'rescued' the speck from the field of clovers after Vlad had dropped it. By picking it up, Horton put Whoville back in danger.
At the end, everyone manages to confront Horton and somehow manage to get to him even though he destroyed a bridge earlier in the film and it was the only way to get across.